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Technical Brief

Stochastic Finite-Time Stabilization for a Class of Nonlinear Markovian Jump Stochastic Systems With Impulsive Effects

[+] Author and Article Information
Wu-Hua Chen

College of Mathematics and Information Science,
Guangxi University,
Nanning, Guangxi 530004, China
e-mail: wuhua_chen@163.com

Chenghai Wei

College of Mathematics and Information Science,
Guangxi University,
Nanning, Guangxi 530004, China
e-mail: wch20100513@163.com

Xiaomei Lu

College of Mathematics and Information Science,
Guangxi University,
Nanning, Guangxi 530004, China
e-mail: lu_xiaomei@126.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 9, 2014; final manuscript received October 16, 2014; published online January 6, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 137(4), 044501 (Apr 01, 2015) (6 pages) Paper No: DS-14-1171; doi: 10.1115/1.4028874 History: Received April 09, 2014; Revised October 16, 2014; Online January 06, 2015

This paper is dedicated to the study of stochastic finite-time stability (SFTS) and control synthesis for a class of nonlinear Markovian jump stochastic systems with impulsive effects. By introducing a time-varying stochastic Lyapunov function with discontinuities at impulse times, an improved criterion for SFTS is derived in terms of linear matrix inequalities (LMIs). Based on the new SFTS criterion, four kinds of finite-time hybrid/continuous-time state feedback controllers are constructed by using the solutions to certain sets of LMIs. The effectiveness of the proposed method is validated through one numerical example.

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